Bulletin of the American Physical Society
69th Annual Meeting of the APS Division of Fluid Dynamics
Volume 61, Number 20
Sunday–Tuesday, November 20–22, 2016; Portland, Oregon
Session R10: Convection and Buoyancy Driven Flows: Planetary & Exoplanetary Dynamics 
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Sponsoring Units: DFD GPC Chair: Ben Brown, University of Colorado Room: B118119 
Tuesday, November 22, 2016 1:30PM  1:43PM 
R10.00001: Convective overshoot at stiffly stable interfaces Benjamin Brown, Jeffrey Oishi, Daniel Lecoanet, Keaton Burns, Geoffrey Vasil Convective overshoot is an important nonlocal mixing and transport process in stars, extending the influence of turbulent stellar convection beyond the unstable portions of the atmosphere. In the Sun, overshoot into the tachocline at the base of the convection zone has been ascribed a major role in the storage and organization of the globalscale magnetic fields within the solar dynamo. In massive stars, overshooting convection plays an important role in setting the lifespan of the star by mixing fuel into the nuclear burning core. Here we narrowly consider the properties of convective overshoot across very stiff interfaces within fully compressible dynamics across convection zones with significant stratification. We conduct these studies using the Dedalus pseudospectral framework. We extend prior studies of overshoot substantially and find that the depth of overshoot in DNS simulations of a typical plume is wellpredicted by a simple buoyancy equilibration model. The implications of this model, extended into the stellar regime, are that very little overshoot should occur under solar conditions. This would seem to sharply limit the role of the tachocline within the global solar dynamo. [Preview Abstract] 
Tuesday, November 22, 2016 1:43PM  1:56PM 
R10.00002: Sustained shear flows in stratified convection Evan Anders, Tayler Quist, Benjamin Brown, Jeffrey Oishi Highly stratified convection is ubiquitous among natural systems including planetary atmospheres and stellar envelopes. Here we study fully compressible convection within planeparallel, polytropically stratified layers using the Dedalus pseudospectral framework at moderate to high Rayleigh number. We find that large scale shearing "zonal" flows can naturally arise in such systems, as previously found in incompressible RayleighBenard convection. These zonal winds can strongly influence the dynamics of convection. We study the forces that drive and dissipate largescale shear flows and the bulk properties of sustained flows. We find naturally occurring shear flows at moderate aspect ratio and explore methods to achieve similar, convectivelydriven shear flows at larger aspect ratios. [Preview Abstract] 
Tuesday, November 22, 2016 1:56PM  2:09PM 
R10.00003: The stability of buoyancydriven gaseous boundary layers over inclined semiinfinite hot plates Prabakaran Rajamanickam, Wilfried Coenen, Antonio L Sanchez The freeconvective boundarylayer flow that develops over a semiinfinite inclined hot plate is known to become unstable at a finite distance from the leading edge, characterized by a critical value of the Grashof number $Gr_\delta$ based on the local boundarylayer thickness $\delta$. The character of the instability depends on the inclination angle $\phi$, measured from the vertical direction. For values of $\phi$ below a critical value $\phi_c$ the instability is characterized by the appearance of spanwise vortices, whereas for $\phi>\phi_c$ the bifurcated flow displays G\"ortlerlike streamwise vortices. The Boussinesq approximation, employed in previous linear stability analyses, ceases to be valid for gaseous flow when the walltoambient temperature ratio $\theta_w=T_w/T_\infty$ is not close to unity. The corresponding nonBoussinesq analysis is presented here, accounting also for the variation with temperature of the different transport properties. The baseflow profiles are used in a parallelflow temporal stability analysis to delineate the dependence of the critical Grashof numbers $Gr_\delta$ on the inclination angles $\phi$ and on the temperature ratio $\theta_w$. The analysis provides in particular the values of the crossover inclination angles $\phi_c(\theta_w)$. [Preview Abstract] 
Tuesday, November 22, 2016 2:09PM  2:22PM 
R10.00004: The formation of thermohaline staircases for large salt concentration differences in double diffusive convection Yantao Yang, Roberto Verzicco, Detlef Lohse In the upper layers of the tropical and subtropical ocean, steplike mean profiles for both temperature and salinity are often observed, a phenomenon referred to as thermohaline staircase. It consists of alternatively stacked mixing layers, and finger layers with sharp gradients in both mean temperature and salinity. It is believed that thermohaline staircases are caused by double diffusive convection (DDC), i.e. the convection flow with fluid density affected by two different scalars. Here we conducted direct numerical simulations of DDC bounded by two parallel plates and aimed to realise the multilayer state similar to the oceanic thermohaline staircase. We applied an unstable salinity difference and a stable temperature difference across the two plates. We gradually increased the salinity Rayleigh number $Ra_S$, i.e. the strength of salinity difference, and fixed the relative strength of temperature difference. When $Ra_S$ is high enough the flow undergoes a transition from a single finger layer to a triple layer state, where one mixing layer emerges between two finger layers. Such triple layer state is stable up to the turbulent diffusive time scale. The fingerlayer height is larger for higher $Ra_S$. The dependences of the scalar fluxes on $Ra_S$ were also investigated. [Preview Abstract] 
Tuesday, November 22, 2016 2:22PM  2:35PM 
R10.00005: Drifting localized structures in doubly diffusive convection Edgar Knobloch, David Lo Jacono, Alain Bergeon We use numerical continuation to compute a multiplicity of spatially localized states in doubly diffusive convection in a vertical slot driven by imposed horizontal temperature and concentration differences. The calculations focus on the socalled opposing case, in which the resulting gradients are in balance. Noslip boundary conditions are used at the sides and periodic boundary conditions with large spatial period are used in the vertical direction. This system exhibits homoclinic snaking of stationary spatially localized structures with point symmetry [1,2]. In this talk we demonstrate the existence, near threshold, of drifting pulses of spatially localized convection that appear when mixed concentration boundary conditions are used, and use homotopic continuation to identify similar states in the case of fixed concentration boundary conditions. We show that these states persist to large values of the Grasshof number and provide a detailed study of their properties. [1] A. Bergeon & E. Knobloch, Phys. Fluids 20, 034102 (2008). [2] C. Beaume, A. Bergeon & E. Knobloch, Phys. Fluids 25, 114102 (2013). [Preview Abstract] 
Tuesday, November 22, 2016 2:35PM  2:48PM 
R10.00006: A reduced model for saltfingering convection in the small Lewis number limit JinHan Xie, Edgar Knobloch We derive a reduced model that captures key features of saltfingering convection, including secondary instabilities, in the asymptotic limit of small Lewis number and large flux ratio. In the infinite Prandtl number limit, this model combines a prognostic equation for the evolution of the salinity field with a novel diagnostic relation between the streamfunction and salinity. When the salinity and temperature Rayleigh numbers $Ra_S$ and $Ra_T$ are large, simulations reveal the existence of statistically steady saturated states, characterized by fluxes and kinetic energy that scale as powers of $(Ra_S/Ra_T)1$. Three distinguished regimes are identified: a weakly nonlinear regime and two strongly nonlinear regimes characterized by distinct exponents. The processes responsible for saturation are described in detail and the probability density function of the saturated fields is determined. [Preview Abstract] 
(Author Not Attending)

R10.00007: Numerical studies of a confined volatile binary fluid subject to a horizontal temperature gradient Tongran Qin, Roman Grigoriev Our fundamental understanding of convection in a layer of nonisothermal binary fluid with free surface in the presence of noncondensable gases, such as air, is still limited. In relatively thick liquid layers, the flow is driven by a combination of three different forces: buoyancy, thermocapillarity, and solutocapillarity in the liquid layer. Unlike buoyancy, both thermocapillarity and solutocapillarity depend sensitively on the boundary conditions at the liquidvapor interface. Recent experimental studies showed that the composition of both the liquid and the gas phases have significant effects on the convection pattern. In particular, in a methanolwater mixture, four different flow regimes were identified on a map spanned by the concentration of methanol in the liquid and the concentration of air in the gas, which are thermocapillaritydominated flow (TDF), solutocapillaritydominated flow (SDF), unsteady flow (UF) and reversed flow (RF). This talk will present a comprehensive numerical model for a confined volatile binary fluid subject to a horizontal temperature gradient in the presence of noncondensable gases, and illustrate how the composition of both phases affect thermocapillarity and solutocapillarity. The numerical results will also be compared with experiments. [Preview Abstract] 
Tuesday, November 22, 2016 3:01PM  3:14PM 
R10.00008: Convectiondriven dynamos in the limit of rapid rotation Michael Calkins, Louie Long, David Nieves, Keith Julien, Steven Tobias Most largescale planetary magnetic fields are thought to be driven by rapidly rotating convection. Direct numerical simulation (DNS) remains an important tool for investigating the physics of dynamos, but remains severely restricted in parameter space relative to geo and astrophysical systems. Asymptotic models provide a complimentary approach to DNS that have the ability to access planetarylike magnetohydrodynamical regimes. We utilize an asymptotic dynamo model to investigate the influence of convective flow regime on dynamo action. We find that the spatial characteristics of the largescale magnetic field are dependent only weakly on changes in flow behavior. In contrast, the behavior of the smallscale magnetic field is directly dependent on, and therefore shows significant variations with, the smallscale convective flow field. These results may suggest why many previous DNS studies, which reside in a vastly different parameter space relative to planets, are nonetheless successful in reproducing many of the observed features of planetary magnetic fields. [Preview Abstract] 
Tuesday, November 22, 2016 3:14PM  3:27PM 
R10.00009: Direct measurement of the heat exchanges in a buoyancy driven twophase flow; application to the planets core formation JeanBaptiste Wacheul, Michael Le Bars Telluric planet formation involved the settling of large amounts of liquid iron coming from impacting planetesimals into a viscous magma ocean as deep as thousands of kilometers. During this ``iron rain'', the initial state of planets was mostly determined by exchanges of heat and elements between the two phases. Most models of planet formation simply assume that the metal rapidly equilibrated with the whole mantle. Here we report the results of experiments on which we performed measurements of the diffusive exchanges integrated during the fall, in addition to measuring the dynamical variables of the flow on high speed videos recordings. Using a balloon filled with liquid gallium alloy as an analogue for the iron core of the impactor and a viscous fluid as an analogue for the silicate magma, we were able to produce flows matching the dynamical regime of the geophysical inspiration. We find that the early representations of this flow as an iron ``rain'' is far from the experiments, both in terms of fluid mechanics and diffusive exchanges during the phase where most of the equilibration is accomplished. Indeed, the equilibration coefficient at a given depth depends both on the size of the metal diapir and on the viscosity of the ambient fluid, whereas the falling speed is only controlled by the size. Various scalings chosen in the literature for the diffusive exchanges, and we find good agreement with the hypothesis and scaling of a turbulent thermal. [Preview Abstract] 
Tuesday, November 22, 2016 3:27PM  3:40PM 
R10.00010: Chemically reacting fluid flow in exoplanet and brown dwarf atmospheres Baylee Bordwell, Benjamin P. Brown, Jeffrey S. Oishi In the past few decades, spectral observations of planets and brown dwarfs have demonstrated significant deviations from predictions in certain chemical abundances. Starting with Jupiter, these deviations were successfully explained to be the effect of fast dynamics on comparatively slow chemical reactions. These dynamical effects are treated using mixing length theory in what is known as the "quench" approximation. In these objects, however, both radiative and convective zones are present, and it is not clear that this approximation applies. To resolve this issue, we solve the fully compressible equations of fluid dynamics in a matched polytropic atmosphere using the stateoftheart pseudospectral simulation framework Dedalus. Through the inclusion of passive tracers, we explore the transport properties of convective and radiative zones, and verify the classical eddy diffusion parameterization. With the addition of active tracers, we examine the interactions between dynamical and chemical processes using abstract chemical reactions. By locating the quench point (the point at which the dynamical and chemical timescales are the same) in different dynamical regimes, we test the quench approximation, and generate prescriptions for the exoplanet and brown dwarf communities. [Preview Abstract] 
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